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Concept explainers
The expression for the steady state voltage vo (t).
The steady state response for the given function is given by,
Given:
The square wave input for the given circuit is given as,
Fourier series approximation and is given by
Transfer function = Where R = 600
and C
Concept Used:
We first calculate magnitude of the given transfer function, phase angle, bandwidth, and magnitude of phase angles of respective frequencies and finally calculate the expression for steady state response.
Calculation:
The Fourier series approximation is given by,
The transfer function of series RC circuit is given by,
The expression for magnitude of transfer function of the given system is,
(1)
Substituting for R = 103 and C =
in equation (1) we get,
The phase angle is given by
.... (3)
Substituting for R = 103 and C =
in equation (3) we get,
.... (4)
The bandwidth for the given system should lie between 0 and
(5)
Substituting R = 103 and C =
in equation (5) we get,
1000 rad/s
As is greater than 1000 rad/s which is outside the required bandwidth, we consider only 0 and 120
for frequency values.
The magnitude value for the frequencies 0and 120 is,
From equation (2) we know that
Substituting for 0 and 120
respectively we get,
(6)
On simplifying we get
0.9357.... (7)
From equation (4) we have
Now calculating the phase angles for corresponding frequencies 0, 240 and 480
respectively we get,
The steady state voltage for the given Fourier series,
is given by,
Conclusion:
Therefore, the steady stat response for the given function is given by
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Chapter 9 Solutions
EBK SYSTEM DYNAMICS
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